## Notes on Topic 15: Correlation: The Relationship of Two Variables

You are watching: A ____ is a visual way to show how two variables relate to each other.

## Correlation Indices and Scatterplots

Definition of Correlation: Correlation is a statistical technique that is used to measure and describe the**STRENGTH**and DIRECTION of the relationship between two variables. Correlation requires two scores from the

**SAME**individuals. These scores are normally identified as X and Y. The pairs of scores can be listed in a table or presented in a scatterplot. Usually the two variables are observed, not manipulated.

Definition of a Scatterplot: A scatterplot is a statistical graphic that displays the STRENGTH, DIRECTION and SHAPE of the relationship between two variables. A scatterplot requires two scores from the SAME individuals. These scores are normally identified as X and Y. A scatterplot displays the X variable on the horizontal (X) axis, and the Y variable on the vertical (Y) axis. Each individual is identified by a single point (dot) on the graph which is located so that the coordinates of the point (the X and Y values) match the individual"s X and Y scores. |

**Example:**Consider the correlation between the SAT-M scores and GPA of the 1997 Psych 30 class. Here are the Math SAT scores and the GPA scores of 13 of the students in the class, and the scatterplot for all 41 students:

Scatterplot: The scatterplot has the X variable (GPA) on the horizontal (X) axis, and the Y variable (MathSAT) on the vertical (Y) axis. Each individual is identified by a single point (dot) on the graph which is located so that the coordinates of the point (the X and Y values) match the individual"s X (GPA) and Y (MathSAT) scores. For example, the student named "Obs5" (in the sixth row of the datasheet) has GPA=2.30 and MathSAT=710. This student is represented in the scatterplot by high-lighted and labled ("5") dot in the upper-left part of the scatterplot. Note that is to the right of MathSAT of 710 and above GPA of 2.30. Pearson Correlation:The Pearson correlation (explained below) between these two variables is .32. Correlations and Scatterplots: Correlations can tell us about the direction, and the degree (strength) of the relationship between two variables. Scatterplots can also tell us about the form (shape) of the relationship. |

**degree (strength) of the relationship between two variables. The Pearson Correlation Coefficient measures the strength of the linear relationship between two variables. Two specific strengths are: Perfect Relationship**: When two variables are exactly (linearly) related the correlation coefficient is either +1.00 or -1.00. They are said to be perfectly linearly related, either positively or negatively. No relationship: When two variables have no relationship at all, their correlation is 0.00. There are strengths in between -1.00, 0.00 and +1.00. Note, though. that +1.00 is the largest postive correlation and -1.00 is the largest negative correlation that is possible. Examples: Here are three examples. These examples concern variables measuring characteristics of automobiles. The variables are their weight, miles-per-gallon, horsepower and drive ratio (number of revolutions of the engine per revolution of the wheels). The relationship between Weight and Horsepower is strong, linear, and positive, though not perfect. The Pearson correlation coefficient is +.92.

Weight and Horsepower |

Drive Ratio and Horsepower |

Drive Ratio and Miles-Per-Gallon |

Miles-per-gallon and engine displacement |

**Where & Why we use Correlation: Correlations are used for Prediction**, Validity, Reliability, and Verification.

See more: Which Intangible Assets Are Amortized Over Their Useful Life Quizlet

We can test this prediction by administering IQ tests to the parents and their children, and measuring the correlation between the two scores.